The associated \(D\) –dimensional terms up to the constant parts were calculated in [1]}, [2]}, see also [3]}, [4]}, and do also agree. This concerns the 1PN correction
to the electric quadrupole moment, \(E Q_{ij} Q_{ji}\) ,[3]}, the octupole moment, \(E O_{ijk}O_{ijk}\) , and the
magnetic quadrupole moment, \(E J_{ij} J_{ji}\) . The angular momentum failed tail,
\(L_k \varepsilon _{ijk} Q_{il} Q_{jl}\) ,
and the memory term, \(Q_{ij} Q_{jk} Q_{ki}\) , are non singular and contribute only local \(O(\nu ^2)\)  terms.
The latter two contributions were calculated in
[1]}, [7]}, however, not using the
Schwinger–Keldysh
formalism (also called in–in or closed time path formalism), which
has been developed
in Refs. [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [7]}.
The angular momentum failed tail had been calculated by us at the time of [2]} obtaining
the same result as in [1]}.
